3.38/1.67	WORST_CASE(NON_POLY, ?)
3.38/1.68	proof of /export/starexec/sandbox2/benchmark/theBenchmark.xml
3.38/1.68	# AProVE Commit ID: 48fb2092695e11cc9f56e44b17a92a5f88ffb256 marcel 20180622 unpublished dirty
3.38/1.68	
3.38/1.68	
3.38/1.68	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.38/1.68	
3.38/1.68	(0) CpxTRS
3.38/1.68	(1) RelTrsToDecreasingLoopProblemProof [LOWER BOUND(ID), 0 ms]
3.38/1.68	(2) TRS for Loop Detection
3.38/1.68	(3) InfiniteLowerBoundProof [FINISHED, 23 ms]
3.38/1.68	(4) BOUNDS(INF, INF)
3.38/1.68	
3.38/1.68	
3.38/1.68	----------------------------------------
3.38/1.68	
3.38/1.68	(0)
3.38/1.68	Obligation:
3.38/1.68	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.38/1.68	
3.38/1.68	
3.38/1.68	The TRS R consists of the following rules:
3.38/1.68	
3.38/1.68	   g(X) -> h(activate(X))
3.38/1.68	   c -> d
3.38/1.68	   h(n__d) -> g(n__c)
3.38/1.68	   d -> n__d
3.38/1.68	   c -> n__c
3.38/1.68	   activate(n__d) -> d
3.38/1.68	   activate(n__c) -> c
3.38/1.68	   activate(X) -> X
3.38/1.68	
3.38/1.68	S is empty.
3.38/1.68	Rewrite Strategy: INNERMOST
3.38/1.68	----------------------------------------
3.38/1.68	
3.38/1.68	(1) RelTrsToDecreasingLoopProblemProof (LOWER BOUND(ID))
3.38/1.68	Transformed a relative TRS into a decreasing-loop problem.
3.38/1.68	----------------------------------------
3.38/1.68	
3.38/1.68	(2)
3.38/1.68	Obligation:
3.38/1.68	Analyzing the following TRS for decreasing loops:
3.38/1.68	
3.38/1.68	The Runtime Complexity (innermost) of the given CpxTRS could be proven to be BOUNDS(INF, INF).
3.38/1.68	
3.38/1.68	
3.38/1.68	The TRS R consists of the following rules:
3.38/1.68	
3.38/1.68	   g(X) -> h(activate(X))
3.38/1.68	   c -> d
3.38/1.68	   h(n__d) -> g(n__c)
3.38/1.68	   d -> n__d
3.38/1.68	   c -> n__c
3.38/1.68	   activate(n__d) -> d
3.38/1.68	   activate(n__c) -> c
3.38/1.68	   activate(X) -> X
3.38/1.68	
3.38/1.68	S is empty.
3.38/1.68	Rewrite Strategy: INNERMOST
3.38/1.68	----------------------------------------
3.38/1.68	
3.38/1.68	(3) InfiniteLowerBoundProof (FINISHED)
3.38/1.68	The following loop proves infinite runtime complexity:
3.38/1.68	
3.38/1.68	The rewrite sequence
3.38/1.68	
3.38/1.68	g(n__c) ->^+ g(n__c)
3.38/1.68	
3.38/1.68	gives rise to a decreasing loop by considering the right hand sides subterm at position [].
3.38/1.68	
3.38/1.68	The pumping substitution is [ ].
3.38/1.68	
3.38/1.68	The result substitution is [ ].
3.38/1.68	
3.38/1.68	
3.38/1.68	
3.38/1.68	
3.38/1.68	----------------------------------------
3.38/1.68	
3.38/1.68	(4)
3.38/1.68	BOUNDS(INF, INF)
3.52/1.75	EOF